Question

hi:) for 5(b) , I got 157.7 & 22.3 but in the answer key, the only correct answer is 157.7. I thought there should be 2 possible values?

Answer 1

Θ = 157.7°

Explanation:

Given

cosΘ = - 0.925

Since cosΘ < 0 then Θ is in the second or third quadrant.

Since 0° ≤ Θ ≤ 180° then Θ is in the second quadrant. thus

Θ =
`cos^(-1)`(- 0.925) = 157.7° ← angle in second quadrant

Answer 2

There should be only 1 value (157.7°) since we reject the second value as θ lies in quadrant 1 and 2. Note that the 2nd value should have been 202.3°, which is greater than 180°.

Cosine of an angle negative in the 2nd and 3rd quadrant.

Explanation:

Please see attached picture.